Details

Time bar (total: 14.6s)

sample105.0ms

Algorithm
intervals
Results
17.0ms33×body2560valid
15.0ms35×body1280valid
15.0ms168×body80valid
12.0ms8×body160valid
8.0ms92×body80nan
5.0ms15×body640valid
4.0ms6×body5120valid
3.0ms9×body320valid

simplify152.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
133.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms
(- (* b b) (* (* 4.0 a) c))
40.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms
(- (* b b) (* (* 4.0 a) c))
94.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01541565
14011461
213531245
done50011233

prune413.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize41.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.6b
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
102.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
129.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series719.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (* b b) (* (* 4.0 a) c))
240.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
278.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
140.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
160 → 160
Iterations

Useful iterations: 2 (729.0ms)

IterNodesCost
02524912
16234364
227804036
done50004036

prune688.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
16.5b
(/ (* 2.0 a) (* (* c 4.0) a))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
33.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(/ (* 2.0 a) (* (* c 4.0) a))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(/ (* 2.0 a) (* (* c 4.0) a))
136.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
82 → 82
Iterations

Useful iterations: 2 (424.0ms)

IterNodesCost
01591332
14221180
22277952
done5001952

prune302.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
13×add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity
10×add-log-exp
9×div-exp
8×pow1
7×add-cube-cbrt
6×prod-exp
5×flip3-- associate-/r/ flip--
4×cbrt-undiv sqrt-prod
3×rec-exp times-frac diff-log 1-exp associate-/l*
2×frac-times sub-neg pow-flip sqrt-div associate-*r/ cbrt-unprod distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ clear-num associate-/r* div-inv inv-pow
Counts
4 → 82
Calls
4 calls:
77.0ms
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series511.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(/ 1 (* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
100.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
55.0ms
(- (* b b) (* (* 4.0 a) c))
114.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
94 → 94
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01731830
14161672
213531462
done50001396

prune294.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 7.2b

regimes296.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.6b

bsearch245.0ms

Steps
ItersRangePoint
5
3.1594096090812424e+104
8.241903478382293e+104
6.2080577970805e+104
8
-4.3193946104502796e-226
-4.381317687258745e-230
-7.892835993842436e-230
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03460
14060
done4060

end0.0ms

sample3.4s

Algorithm
intervals
Results
937.0ms5870×body80valid
525.0ms1051×body2560valid
493.0ms893×body1280valid
463.0ms218×body320valid
226.0ms2845×body80nan
130.0ms480×body640valid
116.0ms98×body5120valid
14.0ms108×body160valid